The reason why most molecular force fields stop at point charges and dipoles is they're good enough.
What we mean by "good enough" is for the electrostatic potential (ESP) around a classical molecular dynamics molecule to be similar enough to the actual ESP (calculated with quantum chemistry). A definitive early article on this is Dykstra's Electrostatic interaction potentials in molecular force fields (Chem. Rev. 1993, 93, 7, 2339–2353; link). It goes into significant detail about the accuracy and cost of higher-order moments; this is not just a matter of not having enough compute (if octopoles were worth talking about in 1993 they're worth talking about now!).
This passage in particular is important:
an exact representation, we seek only one that is correct in the regions of interest. Probably the separation distances where charge field representations need to be most accurate are those from just under the separations associated with van der Waals radii to about twice that distance. ... At closer separations the charge distributions will tend to overlap and make invalid the physical justification for classical electrostatic potentials, and at separations beyond this range the interaction energy and forces are all weak; accuracy in the far-off regions is not important for most force field
So the vast majority of molecular dynamics simulations are okay with point charges. Polarizable dipoles are especially valuable as a relatively cheap model for cooperative effects -- thus, polarisability can accurate capture both a relatively less bound dimer-in-vacuum and the more intensely interacting condensed phase. Higher-order moments, until now, were mostly of interest in people trying to predict IR spectra in silico. Of course, you could argue that the current wave of innovative ML models is (in roundabout way) a fitting to the higher-order near-field octo-and-beyond multiples.